@Article{CiCP-35-4,
author = {Chunyu, Chen and Long, Chen and Xuehai, Huang and Wei, Huayi},
title = {Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements},
journal = {Communications in Computational Physics},
year = {2024},
volume = {35},
number = {4},
pages = {1045--1072},
abstract = {<p style="text-align: justify;">This study investigates high-order face and edge elements in finite element
methods, with a focus on their geometric attributes, indexing management, and practical application. The exposition begins by a geometric decomposition of Lagrange
finite elements, setting the foundation for further analysis. The discussion then extends to $H$(div)-conforming and $H$(curl)-conforming finite element spaces, adopting
variable frames across differing sub-simplices. The imposition of tangential or normal
continuity is achieved through the strategic selection of corresponding bases. The paper concludes with a focus on efficient indexing management strategies for degrees
of freedom, offering practical guidance to researchers and engineers. It serves as a
comprehensive resource that bridges the gap between theory and practice.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0249},
url = {https://global-sci.com/article/90948/geometric-decomposition-and-efficient-implementation-of-high-order-face-and-edge-elements}
}